Finite Group Databasebeta

← #13175846

Subgroups — #13175846

Order 1728.

1804 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723926C211yesmaximal, characteristic, complemented
2C3×#64088C211yesmaximal, characteristic, complemented
3C32×#882C211yesmaximal, characteristic, complemented
4#11723630C211yesmaximal, characteristic, complemented
5#11723614C211yesmaximal, characteristic, complemented
6D3×#3757C211yesmaximal, characteristic, complemented
7#11723599C211yesmaximal, characteristic, complemented
8#11723499C211yesmaximal, characteristic, complemented
9#11723496C211yesmaximal, characteristic, complemented
10#11723475C211yesmaximal, characteristic, complemented
11#11723475C211yesmaximal, characteristic, complemented
12#11723461C211yesmaximal, characteristic, complemented
13#11723432C211yesmaximal, characteristic, complemented
14#11723429C211yesmaximal, characteristic, complemented
15#11723422C211yesmaximal, characteristic, complemented
16#10596064—31nomaximal
17#10594126—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×#6308C2211yescharacteristic, complemented
21C2×C32×#67C2211yescharacteristic
22C2×C32×D12C2211yescharacteristic
23C2×C32×D12C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6291C2211yescharacteristic
26C2×#6291C2211yescharacteristic, complemented
27C2×#6289C2211yescharacteristic, complemented
28C2×D3×C3⋊Dic3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
31C33×C22⋊C4C2211yescharacteristic
32#88864C2211yescharacteristic
33#88859C2211yescharacteristic, complemented
34#88859C2211yescharacteristic, complemented
35C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C3×#3757C2211yescharacteristic
37C3×#3757C2211yescharacteristic
38C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C3×#3750C2211yescharacteristic, complemented
41C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44#88807C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53C32×#120—31no—
54#64162—31no—
55C2×#3757—31no—
56#64148—31no—
57#64148—31no—
58#64147—31no—
59#64145—31no—
60#64144—31no—
61D4×C3⋊Dic3—31no—
62#64094—31no—
63#64094—34no—
64#64094—64no—
65#64092—31no—
66#64090—31no—
67#64088—31no—
68#64088D311yescharacteristic, complemented
69#64087—31no—
70C3×#882D314yescomplemented
71C3×#879—34no—
72#63977—34no—
73#63969—34no—
74D3×#217—34no—
75#63958—34no—
76#63898—34no—
77#63896—34no—
78#63886—34no—
79#63886—34no—
80#63880—34no—
81#63862—34no—
82#63860—34no—
83#63854—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C32×D3—22no—
87C22×C32×D3—41no—
88C22×C32×D3—41no—
89C22×C32×D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94#6312—41no—
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98#6308—41no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C32×#67—41no—
104C2×C32×Dic3C2311yescharacteristic
105C32×D12—22no—
106C32×D12—41no—
107#6291—22no—
108#6291—41no—
109#6291—41no—
110#6289—41no—
111D3×C3⋊Dic3—41no—
112D3×C3⋊Dic3—41no—
113D3×C3⋊Dic3—41no—
114#5704—91no—
115#5593—94no—
116C24×C32—31no—
117C23×C3×D3C2×D314yes—
118C2×C32×D4—31no—
119C2×C32×D4—31no—
120C2×C32×D4—31no—
121C2×#638—31no—
122C2×#638—34no—
123C2×#638—31no—
124C2×#638—31no—
125C2×#638—31no—
126C2×#638—64no—
127C22×C3⋊Dic3—31no—
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—31no—
130C2×C4×C3⋊D3—31no—
131C2×#634—31no—
132C2×#634—34no—
133C2×#634—64no—
134C2×C3×#67C2×D314yes—
135C2×C3×D12C2×D314yes—
136C2×C3×D12C2×D314yes—
137C2×#626—34no—
138C2×#626—34no—
139C2×#626—34no—
140C2×#624—34no—
141C2×D3×Dic3—34no—
142C2×D3×Dic3—34no—
143C2×D3×Dic3—34no—
144C32×C22⋊C4—24no—
145C32×C22⋊C4—31no—
146C32×C22⋊C4—31no—
147C32×C22⋊C4C2×D314yes—
148C32×C22⋊C4C2×D311yescharacteristic
149#3757—31no—
150#3757—34no—
151#3757—31no—
152#3757—31no—
153#3757—31no—
154#3757—31no—
155#3757—31no—
156#3757—31no—
157#3757—64no—
158#3757C2×D311yescharacteristic
159#3757C2×D311yescharacteristic
160#3752—31no—
161#3752—31no—
162#3752—34no—
163#3752—34no—
164#3752—64no—
165#3752—64no—
166C4⋊(C3⋊Dic3)—31no—
167C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
168#3750—31no—
169#3750—31no—
170#3750C2×D311yescharacteristic, complemented
171#3750C2×D311yescharacteristic, complemented
172C4×C3⋊Dic3—31no—
173C4×C3⋊Dic3—34no—
174C4×C3⋊Dic3—64no—
175C4×C3⋊Dic3C2×D311yescharacteristic, complemented
176C3×#217—34no—
177C3×#217—34no—
178C3×(C2×D3)⋊C4C2×D314yes—
179C3×(C2×D3)⋊C4C2×D314yes—
180C3×C4⋊Dic3—34no—
181C3×Dic3⋊C4—34no—
182C3×Dic3⋊C4—34no—
183C3×C4×Dic3—34no—
184#3724—34no—
185Dic3⋊Dic3—34no—
186Dic3⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191(C2×D3)⋊Dic3—34no—
192(C2×D3)⋊Dic3—34no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33C2411yescharacteristic
197C2×C3⋊(C3⋊D3)—21no—
198C2×C3⋊(C3⋊D3)—21no—
199C2×C3⋊(C3⋊D3)—21no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—44no—
209C2×C32×D3#4112yes—
210C33×C4—21no—
211C33×C4—21no—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3⋊(C3⋊Dic3)—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—21no—
217C3×C3⋊Dic3—21no—
218C3×C3⋊Dic3—21no—
219C32×Dic3—21no—
220C3×#126—91no—
221C3×#120—34no—
222#953—94no—
223C2×#217—94no—
224#939—94no—
225#939—94no—
226#938—94no—
227#936—94no—
228#935—94no—
229D4×Dic3—94no—
230#898—91no—
231#896—91no—
232#895—91no—
233#895—91no—
234#894—91no—
235#893—91no—
236#885—94no—
237#885—91no—
238#885—184no—
239#884—91no—
240#883—94no—
241#883—91no—
242#882—91no—
243#882C3⋊D311yescharacteristic, complemented
244#67⋊C4—94no—
245D3×C22⋊C4—91no—
246#879—34no—
247#879—94no—
248#878—94no—
249#875—91no—
250C4×D12—91no—
251C23×C32—24no—
252C23×C32—31no—
253C23×C32—31no—
254C23×C32—31no—
255C23×C32—62no—
256C23×C32—121no—
257C23×C32—121no—
258C23×C32C22×D314yes—
259C23×C32C22×D311yescharacteristic
260C22×C3⋊D3—31no—
261C22×C3⋊D3—34no—
262C22×C3⋊D3—64no—
263C22×C3×D3—28no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3C22×D314yes—
267C22×C3×D3C22×D314yes—
268C22×C3×D3C22×D314yes—
269C32×D4—62no—
270C32×D4—121no—
271C32×D4—121no—
272C2×C32×C4—24no—
273C2×C32×C4—24no—
274C2×C32×C4—31no—
275C2×C32×C4C22×D314yes—
276C2×C32×C4C22×D314yes—
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C22×D311yescharacteristic
279#638—62no—
280#638—121no—
281#638—121no—
282#638—121no—
283#638—124no—
284#638—128no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—31no—
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—34no—
290C2×C3⋊Dic3—34no—
291C2×C3⋊Dic3—64no—
292C2×C3⋊Dic3—64no—
293C2×C3⋊Dic3—64no—
294C2×C3⋊Dic3—121no—
295C2×C3⋊Dic3—121no—
296C2×C3⋊Dic3—121no—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C4×C3⋊D3—121no—
302#634—121no—
303#634—124no—
304#634—128no—
305C3×#67—44no—
306C2×C3×Dic3—34no—
307C2×C3×Dic3—34no—
308C2×C3×Dic3—34no—
309C2×C3×Dic3—34no—
310C2×C3×Dic3C22×D314yes—
311C3×D12—28no—
312C3×D12—44no—
313#626—68no—
314#626—124no—
315#626—124no—
316#624—124no—
317D3×Dic3—124no—
318D3×Dic3—124no—
319D3×Dic3—124no—
320#538—271noSylow
321C2×C33—41no—
322C2×C33C2×#4111yescharacteristic
323C2×C33H(5,𝔽2)11yescharacteristic
324C2×C33H(5,𝔽2)11yescharacteristic
325C3⋊(C3⋊D3)—41no—
326C32×D3—22no—
327C32×D3—41no—
328C32×D3—41no—
329C24×C3—34no—
330C23×D3C2×C3⋊D311yescharacteristic
331C2×C3×D4—34no—
332C2×C3×D4—34no—
333C2×C3×D4—34no—
334C2×#67—94no—
335C2×#67—94no—
336C2×#67—94no—
337C2×#67—94no—
338C2×#67—91no—
339C2×#67—184no—
340C2×#67C2×C3⋊D311yescharacteristic
341C22×Dic3—94no—
342C22×Dic3—94no—
343C22×Dic3—94no—
344C2×D12—91no—
345C2×D12—91no—
346C2×D12—91no—
347C2×D12C2×C3⋊D311yescharacteristic
348C2×D12C2×C3⋊D311yescharacteristic
349C2×C4×D3—94no—
350C2×C4×D3—91no—
351C2×C4×D3—91no—
352C2×C4×D3—91no—
353C2×C4×D3—91no—
354C2×Dic6—94no—
355C2×Dic6—91no—
356C2×Dic6—184no—
357C3×C4⋊C4—91no—
358C3×C4⋊C4—91no—
359C3×C4⋊C4—91no—
360C3×C22⋊C4—24no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—34no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4D3214yes—
366C3×C22⋊C4C2×C3⋊D311yescharacteristic
367C3×C42—91no—
368#217—34no—
369#217—34no—
370#217—94no—
371#217—94no—
372#217—94no—
373#217—94no—
374#217—94no—
375#217—94no—
376#217—94no—
377#217—91no—
378#217—184no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—94no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—184no—
390(C2×D3)⋊C4—184no—
391(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
392(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
393C4⋊Dic3—34no—
394C4⋊Dic3—94no—
395C4⋊Dic3—91no—
396Dic3⋊C4—34no—
397Dic3⋊C4—34no—
398Dic3⋊C4—94no—
399Dic3⋊C4—94no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402C4×Dic3—34no—
403C4×Dic3—94no—
404C4×Dic3—91no—
405C4×Dic3—184no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—24no—
410C22×C32—24no—
411C22×C32—24no—
412C22×C32—24no—
413C22×C32—32no—
414C22×C32—44no—
415C22×C32—44no—
416C22×C32—44no—
417C22×C32—61no—
418C22×C32—61no—
419C22×C32—61no—
420C22×C32—61no—
421C22×C32—61no—
422C22×C32—61no—
423C22×C32—61no—
424C22×C32—61no—
425C22×C32—124no—
426C22×C32C23×D314yes—
427C22×C32C23×D311yescharacteristic
428C2×C3⋊D3—61no—
429C2×C3⋊D3—61no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—64no—
433C2×C3⋊D3—64no—
434C2×C3⋊D3—124no—
435C2×C3⋊D3—124no—
436C2×C3⋊D3—124no—
437C2×C3×D3—24no—
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—24no—
441C2×C3×D3—24no—
442C2×C3×D3—24no—
443C2×C3×D3—24no—
444C2×C3×D3—24no—
445C2×C3×D3—416no—
446C2×C3×D3#23718yes—
447C32×C4—21no—
448C32×C4—21no—
449C32×C4—24no—
450C32×C4—24no—
451C32×C4—44no—
452C32×C4—44no—
453C32×C4—61no—
454C3⋊Dic3—21no—
455C3⋊Dic3—21no—
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
458C3⋊Dic3—68no—
459C3⋊Dic3—64no—
460C3⋊Dic3—61no—
461C3⋊Dic3—61no—
462C3⋊Dic3—61no—
463C3⋊Dic3—64no—
464C3⋊Dic3—64no—
465C3⋊Dic3—124no—
466C3⋊Dic3—124no—
467C3×Dic3—24no—
468C3×Dic3—64no—
469C3×Dic3—64no—
470C3×Dic3—64no—
471C3×Dic3—64no—
472#126—91no—
473#126—271no—
474#124—271no—
475#124—271no—
476#123—271no—
477#123—271no—
478C22⋊Q8—271no—
479#121—271no—
480#121—271no—
481#121—271no—
482#120—31no—
483#120—271no—
484C4×D4—271no—
485C4×D4—271no—
486C2×C22⋊C4—271no—
487C33#53811yescharacteristic, complemented, Sylow
488C23×C3—24no—
489C23×C3—34no—
490C23×C3—34no—
491C23×C3—34no—
492C23×C3—68no—
493C23×C3—124no—
494C23×C3—124no—
495C23×C3C2×D3214yes—
496C23×C3C22×C3⋊D311yescharacteristic
497C22×D3—22no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—94no—
501C22×D3—91no—
502C22×D3—184no—
503C22×D3C22×C3⋊D311yescharacteristic
504C22×D3C22×C3⋊D311yescharacteristic
505C22×D3C22×C3⋊D311yescharacteristic
506C3×D4—68no—
507C3×D4—124no—
508C3×D4—124no—
509C2×C3×C4—24no—
510C2×C3×C4—24no—
511C2×C3×C4—34no—
512C2×C3×C4—91no—
513C2×C3×C4—91no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4C2×D3214yes—
517C2×C3×C4C2×D3214yes—
518C2×C3×C4C22×C3⋊D311yescharacteristic
519C2×C3×C4C22×C3⋊D311yescharacteristic
520#67—41no—
521#67—188no—
522#67—364no—
523#67—364no—
524#67—364no—
525#67—361no—
526#67—368no—
527C2×Dic3—34no—
528C2×Dic3—34no—
529C2×Dic3—34no—
530C2×Dic3—34no—
531C2×Dic3—94no—
532C2×Dic3—94no—
533C2×Dic3—94no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—184no—
538C2×Dic3—184no—
539C2×Dic3—184no—
540C2×Dic3—364no—
541C2×Dic3—364no—
542C2×Dic3—364no—
543C2×Dic3C22×C3⋊D311yescharacteristic
544D12—22no—
545D12—41no—
546D12—182no—
547D12—361no—
548D12—361no—
549C4×D3—361no—
550C4×D3—364no—
551C4×D3—361no—
552C4×D3—361no—
553C4×D3—361no—
554Dic6—364no—
555Dic6—361no—
556Dic6—368no—
557C2×C32—24no—
558C2×C32—24no—
559C2×C32—24no—
560C2×C32—41no—
561C2×C32—44no—
562C2×C32—62no—
563C2×C32—84no—
564C2×C32—121no—
565C2×C32—121no—
566C2×C32C2×#23714yes—
567C2×C32#100414yes—
568C2×C32#100414yes—
569C2×C32D3×#4111yescharacteristic
570C2×C32#100911yescharacteristic
571C2×C32#100911yescharacteristic
572C3⋊D3—121no—
573C3⋊D3—124no—
574C3⋊D3—244no—
575C3×D3—28no—
576C3×D3—44no—
577C3×D3—44no—
578C24—31no—
579C2×Q8—271no—
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—271no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C22×C4—271no—
588C22×C4—271no—
589C22×C4—271no—
590C22×C4—271no—
591C4⋊C4—91no—
592C4⋊C4—91no—
593C4⋊C4—91no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—91no—
600C22⋊C4—91no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4D3×C3⋊D311yescharacteristic
611C42—91no—
612C42—271no—
613C22×C3—24no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—24no—
620C22×C3—38no—
621C22×C3—44no—
622C22×C3—44no—
623C22×C3—44no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—64no—
627C22×C3—64no—
628C22×C3—64no—
629C22×C3—64no—
630C22×C3—64no—
631C22×C3—64no—
632C22×C3—1216no—
633C22×C3C22×D3214yes—
634C22×C3C23×C3⋊D311yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—44no—
644C2×D3—184no—
645C2×D3—184no—
646C2×D3—184no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—364no—
651C2×D3—364no—
652C2×D3—364no—
653C2×D3#383012yes—
654C3×C4—24no—
655C3×C4—24no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—44no—
659C3×C4—44no—
660C3×C4—64no—
661C3×C4—181no—
662C3×C4—181no—
663C3×C4—181no—
664C3×C4—181no—
665Dic3—21no—
666Dic3—64no—
667Dic3—64no—
668Dic3—64no—
669Dic3—64no—
670Dic3—188no—
671Dic3—184no—
672Dic3—184no—
673Dic3—184no—
674Dic3—181no—
675Dic3—181no—
676Dic3—181no—
677Dic3—364no—
678Dic3—364no—
679C32—24no—
680C32#559314yescomplemented
681C32#570411yescharacteristic, complemented
682C23—31no—
683C23—31no—
684C23—31no—
685C23—62no—
686C23—121no—
687C23—121no—
688C23—271no—
689C23C2×D3×C3⋊D311yescharacteristic
690Q8—1081no—
691D4—62no—
692D4—121no—
693D4—121no—
694D4—542no—
695D4—1081no—
696D4—1081no—
697D4—1081no—
698C2×C4—31no—
699C2×C4—91no—
700C2×C4—91no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—271no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—1081no—
707C2×C4—1081no—
708C2×C4—1081no—
709C2×C4—1081no—
710C2×C4C2×D3×C3⋊D311yescharacteristic
711C2×C4C2×D3×C3⋊D311yescharacteristic
712C2×C3—24no—
713C2×C3—24no—
714C2×C3—24no—
715C2×C3—44no—
716C2×C3—41no—
717C2×C3—68no—
718C2×C3—84no—
719C2×C3—124no—
720C2×C3—124no—
721C2×C3#6430714yes—
722C2×C3D3×#23714yes—
723C2×C3#6431414yes—
724C2×C3C2×#383011yescharacteristic
725C2×C3#6436111yescharacteristic
726C2×C3#6436111yescharacteristic
727D3—22no—
728D3—41no—
729D3—41no—
730D3—364no—
731D3—361no—
732D3—724no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—32no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—61no—
745C22—124no—
746C22—541no—
747C22—541no—
748C22—541no—
749C22C22×D3×C3⋊D311yescharacteristic
750C4—21no—
751C4—21no—
752C4—61no—
753C4—181no—
754C4—181no—
755C4—181no—
756C4—181no—
757C4—541no—
758C4—541no—
759C4—541no—
760C3—24no—
761C3#1059412614yescomplemented
762C3#1059606411yescharacteristic, complemented
763C2—41no—
764C2—62no—
765C2—121no—
766C2—121no—
767C2—1081no—
768C2#1172457911yescharacteristic
769C2D3×#383011yescharacteristic
770C2#1172458811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11723926C2semidirect
2. C3×#64088C2semidirect
3. C32×#882C2semidirect
4. #11723630C2semidirect
5. #11723614C2semidirect
6. D3×#3757C2semidirect
7. #11723599C2semidirect
8. #11723499C2semidirect
9. #11723496C2semidirect
10. #11723475C2semidirect
11. #11723475C2semidirect
12. #11723461C2semidirect
13. #11723432C2semidirect
14. #11723429C2semidirect
15. #11723422C2semidirect
20. C2×#6308C22semidirect
26. C2×#6291C22semidirect
27. C2×#6289C22semidirect
30. C2×D3×C3⋊Dic3C22semidirect
33. #88859C22semidirect
34. #88859C22semidirect
35. C4×C3⋊(C3⋊Dic3)C22semidirect
38. C3×C4⋊(C3⋊Dic3)C22semidirect
39. C3×#3750C22semidirect
40. C3×#3750C22semidirect
41. C3×C4×C3⋊Dic3C22semidirect
44. #88807C22semidirect
45. #88806C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
68. #64088D3semidirect
70. C3×#882D3semidirect
167. C4⋊(C3⋊Dic3)C2×D3semidirect
170. #3750C2×D3semidirect
171. #3750C2×D3semidirect
175. C4×C3⋊Dic3C2×D3semidirect
243. #882C3⋊D3semidirect
487. C33#538semidirect
680. C32#5593semidirect
681. C32#5704semidirect
761. C3#10594126semidirect
762. C3#10596064semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117239262
C3×#640882
C32×#8822
#117236302
#117236142
D3×#37572
#117235992
#117234992
#117234962
#117234752
#117234612
#117234322
#117234292
#117234222
#105960643
#105941263